Unit Cell Modelling

Geometric modelling of a unit cell and its meshing can be obtained using this package. This task is accomplished using an open source code, gmsh in the background.

Note: Here, unit cell implies any spatially repeating rectangular/cuboid domain. It may have inclusions of various shapes and their spatial arrangement may follow any distribution.

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Installation

julia> ]add https://github.com/338rajesh/UnitCellModelling.jl 

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Usage

This module exports the following functions.

make_unit_cell_model(unit_cell; <kwargs>)
plot_nodal_fields(uc_odb, load_case_IDs, nodal_fvariables; <kwargs>)

• unit_cell::AbstractUnitCell

  Defining an unit cell requires a bbox and inclusion geometry data. This information is supplied to modelling process using this unit_cell argument. For example, the following lines define a 3D unit cell of unidirectional composite with circular fibres.

  julia> using UnitCellModelling
  julia> uc_bbox = UnitCellModelling.BBox3D(-1.0,-1.0,-0.2, 1.0, 1.0, 0.2)
  julia> uc_incl_data = Dict("CIRCLE" => [0.0 0.0 0.15; 0.5, 0.5 0.5 0.2])
  julia> unit_cell = UnitCellModelling.UDC3D(uc_bbox, uc_incl_data)

  Note, from the BBox3D definition, that the unit cell dimensions are 2.0, 2.0, 0.4 in x, y, z directions and its centre is at the origin. Also, two circles with radii 0.15 and 0.2 are placed at (0.0, 0.0) and (0.5, 0.5)

  AbstractUnitCell has three subtypes UDC2D, UDC3D, PRC. Also, another two types UDC = Union{UDC2D, UDC3D} and UnitCell3D = Union{UDC3D, PRC} are defined for convenience.

• kwargs, Keyword Arguments

  • small_parameter::Float64 = 1e-06,

    this parameter is used wherever the geometric precision is considered during the modelling process.

  • geom_export_paths::Tuple{Vararg{String}} = (),

    Unit cell can be exported in various formats such as .step, .brep,...etc.

  • extrusion_direction::String = "XY->Z",

    For example, with "XY->Z", Unit cell is first modelled in XY plane and then extruded in Z direction.

  • extr_dir_num_ele::Vector{Int64} = Int64[],

    Number of elements in the direction of extrusion/thickness. This is applicable only when mesh is generated with extrusion.

  • extr_dir_cum_heights::Vector{Float64} = Float64[],

    Cumulative height of elements in the extrusion/thickness direction. For example, with extr_dir_num_ele=3, cumulative heights [0.2, 0.6, 1.0] imply that element thickness take 20%, 40% and 40% thickness.

  • extr_dir_recombine_ele::Bool = true,

  • mesh_periodicity::Bool = true,

  • element_types::Tuple{Vararg{Symbol}} = (:DEFAULT,),

  • min_ele_size_factor::Float64 = 1.0,

  • max_ele_size_factor::Float64 = 2.0,

  • mesh_opt_algorithm::String = "Netgen",

  • show_mesh_stats::Bool = true,

  • node_renum_algorithm = "RCM", Empty string "" avoids renumbering the nodes.

  • show_rve::Bool = true,

• Returns

  A dictionary with the following key-value pairs.

  • "mesh_data" being the key, value is a dictionary with the following key-value pairs,
    • "all_node_tags" => Vector{Int}
    • "all_node_coordinates" => Matrix{Float64}
    • "matrix_element_connectivity" => Matrix{Int}
    • "inclusions_element_connectivity" => Matrix{Int}
    • "total_nodes" => Int
    • "num_2D_elements" => Int
    • "num_3D_elements" => Int

Acceptable inclusion shapes

• 2D shapes:
  • "CIRCLE"
  • "CAPSULE"
  • "RECTANGLE"
  • "ELLIPSE"
  • "REGULARPOLYGON"
  • "CSHAPE"
  • "NLOBESHAPE"

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As of now, fibres with the following shapes can be modelled,

1. Circles add_circular_discs()
2. Regular Polygon make_rpolygon() or add_rpolygons()
3. Capsule make_capsule() or add_capsular_discs()
4. Ellipse make_ellipse() or add_elliptical_discs()
5. Rectangle make_rectangle() or add_rectangular_discs()